Computation With Finitely Presented Groups
Download Computation With Finitely Presented Groups full books in PDF, epub, and Kindle. Read online free Computation With Finitely Presented Groups ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads.
Author |
: Charles C. Sims |
Publisher |
: Cambridge University Press |
Total Pages |
: 624 |
Release |
: 1994-01-28 |
ISBN-10 |
: 9780521432139 |
ISBN-13 |
: 0521432138 |
Rating |
: 4/5 (39 Downloads) |
Synopsis Computation with Finitely Presented Groups by : Charles C. Sims
Research in computational group theory, an active subfield of computational algebra, has emphasised three areas: finite permutation groups, finite solvable groups, and finitely presented groups. This book deals with the third of these areas. The author emphasises the connections with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, computational number theory, and computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms from computational number theory are used to study the abelian quotients of a finitely presented group. The work of Baumslag, Cannonito and Miller on computing nonabelian polycyclic quotients is described as a generalisation of Buchberger's Gröbner basis methods to right ideals in the integral group ring of a polycyclic group. Researchers in computational group theory, mathematicians interested in finitely presented groups and theoretical computer scientists will find this book useful.
Author |
: Volker Diekert |
Publisher |
: Walter de Gruyter GmbH & Co KG |
Total Pages |
: 252 |
Release |
: 2024-10-07 |
ISBN-10 |
: 9783111473574 |
ISBN-13 |
: 3111473570 |
Rating |
: 4/5 (74 Downloads) |
Synopsis Finitely Presented Groups by : Volker Diekert
This book contains surveys and research articles on the state-of-the-art in finitely presented groups for researchers and graduate students. Overviews of current trends in exponential groups and of the classification of finite triangle groups and finite generalized tetrahedron groups are complemented by new results on a conjecture of Rosenberger and an approximation theorem. A special emphasis is on algorithmic techniques and their complexity, both for finitely generated groups and for finite Z-algebras, including explicit computer calculations highlighting important classical methods. A further chapter surveys connections to mathematical logic, in particular to universal theories of various classes of groups, and contains new results on countable elementary free groups. Applications to cryptography include overviews of techniques based on representations of p-groups and of non-commutative group actions. Further applications of finitely generated groups to topology and artificial intelligence complete the volume. All in all, leading experts provide up-to-date overviews and current trends in combinatorial group theory and its connections to cryptography and other areas.
Author |
: Derek F. Holt |
Publisher |
: CRC Press |
Total Pages |
: 532 |
Release |
: 2005-01-13 |
ISBN-10 |
: 9781420035216 |
ISBN-13 |
: 1420035215 |
Rating |
: 4/5 (16 Downloads) |
Synopsis Handbook of Computational Group Theory by : Derek F. Holt
The origins of computation group theory (CGT) date back to the late 19th and early 20th centuries. Since then, the field has flourished, particularly during the past 30 to 40 years, and today it remains a lively and active branch of mathematics. The Handbook of Computational Group Theory offers the first complete treatment of all the fundame
Author |
: Matthew Auger |
Publisher |
: |
Total Pages |
: 88 |
Release |
: 2011 |
ISBN-10 |
: OCLC:746125871 |
ISBN-13 |
: |
Rating |
: 4/5 (71 Downloads) |
Synopsis Methods for Investigating Finitely-presented Groups by : Matthew Auger
This thesis concerns computation with finite group presentations and its application to resolve certain open problems of Kim and Kostrikin. We use the low-index subgroups and abelian quotient invariants algorithms to show that each member of a certain family of finitely-pesented groups is infinite. We present a new algorithm for determining which generalised dihedral groups are quotients of a given finitely-presented group, and use this to show that the groups in another family are pairwise non-isomorphic. Also we describe the method of 'pictures' over group presentations, discussing what they represent and how they can be used to obtain information about the group.
Author |
: René Hartung |
Publisher |
: |
Total Pages |
: 0 |
Release |
: 2012 |
ISBN-10 |
: OCLC:930845614 |
ISBN-13 |
: |
Rating |
: 4/5 (14 Downloads) |
Synopsis Computation with Finitely L-presented Groups by : René Hartung
Author |
: Larry Finkelstein, William M. Kantor |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 404 |
Release |
: |
ISBN-10 |
: 0821885774 |
ISBN-13 |
: 9780821885772 |
Rating |
: 4/5 (74 Downloads) |
Synopsis Groups and Computation II by : Larry Finkelstein, William M. Kantor
The workshop "Groups and Computations" took place at the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) at Rutgers University in June 1995. This and an earlier workshop held in October 1991 was aimed at merging theory and practice within the broad area of computation with groups. The primary goal of the previous workshop was to foster a dialogue between researchers studying the computational complexity of group algorithms and those engaged in the development of practical software. It was expected that this would lead to a deeper understanding of the mathematical issues underlying group computation and that this understanding would lead, in turn, to faster algorithms. Comments and subsequent work indicated that this goal had been achieved beyond expectations. The second workshop was designed to reinforce the progress in these directions. The scientific program consisted of invited lectures and research announcements, as well as informal discussions and software demonstrations. The eight extended talks discussed randomization, permutation groups, matrix groups, software systems, fast Fourier transforms and their applications to signal processing and data analysis, computations with finitely presented groups, and implementation and complexity questions. As in the previous workshop, speakers ranged from established researchers to graduate students.
Author |
: Nathaniel Dean |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 416 |
Release |
: |
ISBN-10 |
: 0821870610 |
ISBN-13 |
: 9780821870617 |
Rating |
: 4/5 (10 Downloads) |
Synopsis Computational Support for Discrete Mathematics by : Nathaniel Dean
With recent technological advances in workstations, graphics, graphical user interfaces, and object oriented programming languages, a significant number of researchers are developing general-purpose software and integrated software systems for domains in discrete mathematics, including graph theory, combinatorics, combinatorial optimization, and sets. This software aims to provide effective computational tools for research, applications prototyping, and teaching. In March 1992, DIMACS sponsored a workshop on Computational Support for Discrete Mathematics in order to facilitate interactions between the researchers, developers, and educators who work in these areas. Containing refereed papers based on talks presented at the workshop, this volume documents current and past research in these areas and should provide impetus for new interactions.
Author |
: Ákos Seress |
Publisher |
: Cambridge University Press |
Total Pages |
: 292 |
Release |
: 2003-03-17 |
ISBN-10 |
: 052166103X |
ISBN-13 |
: 9780521661034 |
Rating |
: 4/5 (3X Downloads) |
Synopsis Permutation Group Algorithms by : Ákos Seress
Table of contents
Author |
: Peter Huxford |
Publisher |
: |
Total Pages |
: |
Release |
: 2018 |
ISBN-10 |
: OCLC:1091435821 |
ISBN-13 |
: |
Rating |
: 4/5 (21 Downloads) |
Synopsis Computation with Finitely Generated Abelian Groups by : Peter Huxford
"Introduction: This aim of this report is to explain the theory of finitely generated abelian groups, and some computational methods pertaining to them. Knowledge of introductory group theory is required to understand the main ideas. There is no algorithm to determine if a given finite presentation defines a group of finite order (or even defines the trivial group). However, such an algorithm exists if the group is also known to be abelian. We give a procedure in this report which, given a description of a finitely generated abelian group G, calculates integers d1,...,dr, k such that G ≥= Zd1 ü ··· ü Zdr ü Zk. The description of G is given by an integer matrix, which we transform into a diagonal matrix, known as its Smith Normal Form. Naive algorithms inspired by Gaussian elimination often fail because of integer overflow. Intermediate matrices have entries which are very large even for relatively small inputs, making calculations in practice far too expensive to carry out. We will explore some useful techniques, which allow us to perform calculations with respect to an appropriate modulus."--Page 1.
Author |
: Larry Finkelstein |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 402 |
Release |
: 1997 |
ISBN-10 |
: 9780821805169 |
ISBN-13 |
: 0821805169 |
Rating |
: 4/5 (69 Downloads) |
Synopsis Groups and Computation II by : Larry Finkelstein
The workshop "Groups and Computations" took place at the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) at Rutgers University in June 1995. This and an earlier workshop held in October 1991 was aimed at merging theory and practice within the broad area of computation with groups. The primary goal of the previous workshop was to foster a dialogue between researchers studying the computational complexity of group algorithms and those engaged in the development of practical software. It was expected that this would lead to a deeper understanding of the mathematical issues underlying group computation and that this understanding would lead, in turn, to faster algorithms. Comments and subsequent work indicated that this goal had been achieved beyond expectations. The second workshop was designed to reinforce the progress in these directions. The scientific program consisted of invited lectures and research announcements, as well as informal discussions and software demonstrations. The eight extended talks discussed randomization, permutation groups, matrix groups, software systems, fast Fourier transforms and their applications to signal processing and data analysis, computations with finitely presented groups, and implementation and complexity questions. As in the previous workshop, speakers ranged from established researchers to graduate students.